Active Viscoelasticity of Sarcomeres

MINI REVIEW published: 14 June 2018 doi: 10.3389/frobt.2018.00069 Frontiers in Robotics and AI | www.frontiersin.org 1 June 2018 | Volume 5 | Article 69 Edited by: Monica A. Daley, Royal Veterinary College, United Kingdom Reviewed by: Eric D. Tytell, Tufts University, United States Allison Arnold, Harvard University, United States Gregory S. Sawicki, University of North Carolina at Chapel Hill, United States *Correspondence: Madhusudhan Venkadesan [email protected] † These authors have contributed equally to this work. Specialty section: This article was submitted to Bionics and Biomimetics, a section of the journal Frontiers in Robotics and AI Received: 23 December 2017 Accepted: 25 May 2018 Published: 14 June 2018 Citation: Nguyen KD, Sharma N and Venkadesan M (2018) Active Viscoelasticity of Sarcomeres. Front. Robot. AI 5:69. doi: 10.3389/frobt.2018.00069 Active Viscoelasticity of Sarcomeres Khoi D. Nguyen † , Neelima Sharma † and Madhusudhan Venkadesan* Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, United States The perturbation response of muscle is important for the versatile, stable and agile control capabilities of animals. Muscle resists being stretched by developing forces in the passive tissues and in the active crossbridges. This review focuses on the active perturbation response of the sarcomere. The active response exhibits typical stress relaxation, and thus approximated by a Maxwell material that has a spring and dashpot arranged in series. The ratio of damping to stiffness in this approximation defines the relaxation timescale for dissipating stresses that are developed in the crossbridges due to external perturbations. Current understanding of sarcomeres suggests that stiffness varies nearly linearly with neural excitation, but not much is known about damping. But if both stiffness and damping have the same functional (linear or not) dependence on neural excitation, then the stress relaxation timescale cannot be varied depending on the demands of the task. This implies an unavoidable and biologically unrealistic trade-off between how freely the crossbridges can yield and dissipate stresses when stretched (injury avoidance in agile motions) vs. how long they can maintain perturbation-induced stresses and behave like a solid material (stiffness maintenance for stability). We hypothesize that muscle circumvents this trade-off by varying damping in a nonlinear manner with neural excitation, unlike stiffness that varies linearly. Testing this hypothesis requires new experimental and mathematical characterization of muscle mechanics, and also identifies new design goals for robotic actuators. Keywords: muscle viscoelasticity, sarcomere mechanics, active perturbation response, variable impedance, stress relaxation timescale, dynamic modulus, sinusoidal response 1. INTRODUCTION A muscle develops mechanical forces when neurally or electrically excited, and also when externally perturbed (Rack and Westbury, 1974; Kirsch et al., 1994; Lindstedt and Hoppeler, 2016). The perturbation response F p of passive tissues and the active excitation-dependent perturbation response F a add to the baseline force F a generated due to neural excitations and to F p due to passive tissues (Figure 1A). Passive refers to mechanical responses in the absence of neural stimulation while active responses require neural stimulation, and consume metabolic energy. Notably, the active resistance to stretch is one of the first mechanical responses of muscle when stimulated, even before it begins to develop tension (McMahon, 1984). Active and passive perturbation responses play an essential role in animal motor control because they are faster than any neural response, including the fastest of reflexes (Bizzi et al., 1982; Brown and Loeb, 2000; Dickinson et al., 2000; Hogan and Buerger, 2005; Holmes et al., 2006; Nishikawa et al., 2007; Biewener, 2016; Roberts, 2016). These responses have also been called preflexes or mechanical feedback (Brown and Loeb, 2000; Nishikawa et al., 2007). In robotics as well, the perturbation response of actuators are employed advantageously when appropriately tuned to the task and the environment’s mechanical response (Hogan, 1984; Pratt and Williamson, 1995; Hogan and Buerger, 2005; Buerger and Hogan, 2007; Vanderborght et al., 2013). However, current actuator